High-order gas kinetic flux solver for simulation of two dimensional incompressible flows

Yang, Liming; Chen, Shu; Жен, Чен; Liu, Y. Y.; Wang, Y.; Shen, Xiang

doi:10.1063/5.0032488

Cited by 9 publications

(1 citation statement)

References 68 publications

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“…Then, it was further developed on triangular meshes and extended to the NS equations by combining the single-stage third-order gaskinetic flux solver (GKS) 13 . Although other solvers, such as the GRP solver, 14,15 can also be adopted, this study still uses the GKS solver but with second-order accuracy 16,17 for the flux construction because the inviscid and viscous flux are coupled and computed simultaneously [18][19][20] . Besides, a series of unified gas-kinetic scheme (UGKS) has been developed for the entire flow regime from the continuum flow to the highly rarefied flow [21][22][23][24] .…”

Section: Introductionmentioning

confidence: 99%

Two-stage Fourth-order Gas Kinetic Solver-based Compact Subcell Finite Volume Method for Compressible Flows over Triangular Meshes

Zhang,

Li,

Song

et al. 2021

Preprint

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To meet the demand for complex geometries and high resolutions of small-scale flow structures, a two-stage fourthorder subcell finite volume (SCFV) method combining the gas-kinetic solver (GKS) with subcell techniques for compressible flows over (unstructured) triangular meshes was developed to improve the compactness and efficiency. Compared to the fourth-order GKS-based traditional finite volume (FV) method, the proposed method realizes compactness effectively by subdividing each cell into a set of subcells or control volumes (CVs) and selecting only face-neighboring cells for high-order compact reconstruction. Because a set of CVs share a solution polynomial, the reconstruction is more efficient than that for traditional FV-GKS, where each CV needs to be separately reconstructed. Unlike in the single-stage third-order SCFV-GKS, both accuracy and efficiency are improved significantly by two-stage fourth-order temporal discretization, for which only a second-order gas distribution function is needed to simplify the construction of the flux function and reduce computational costs. For viscous flows, it is not necessary to compute the viscous term with GKS. Compared to the fourth-stage Runge-Kutta method, one half of the stage is saved for achieving fourth-order time accuracy, which also helps to improve the efficiency. Therefore, a new high-order method with compactness, efficiency, and robustness is proposed by combining the SCFV method with the two-stage gas-kinetic flux. Several benchmark cases were tested to demonstrate the performance of the method in compressible flow simulations.

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Section: Introductionmentioning

confidence: 99%

Two-stage Fourth-order Gas Kinetic Solver-based Compact Subcell Finite Volume Method for Compressible Flows over Triangular Meshes

Zhang,

Li,

Song

et al. 2021

Preprint

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A high-order implicit least square-based finite difference-finite volume method for incompressible flows on unstructured grids

et al. 2021

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In this study, a high-order implicit least squares-based finite difference-finite volume (ILSFD-FV) method with a lattice Boltzmann flux solver is presented for the simulation of two-dimensional incompressible flows on unstructured grids. In this method, a high-order polynomial based on Taylor series expansion is applied within each control cell, where the unknown spatial derivatives at each cell center are approximated by the least squares-based finite difference scheme. The volume integral of the high-order polynomial over the control cell results in a pre-multiplied coefficient matrix in the time-dependent term. This makes the high-order method be implicit in nature. With this feature, a high-order implicit Runge–Kutta time integration scheme, namely, the explicit first-stage singly diagonally implicit Runge–Kutta (ESDIRK) scheme, is applied to obtain the time-accurate solutions for flow problems. The non-linear system of equations arising from each ESDIRK stage except for the first explicit stage is solved by a dual time stepping approach. A matrix-free lower-upper symmetric Gauss–Seidel solver is then used to efficiently march the solution in the pseudo time. The present high-order ILSFD-FV method is verified and validated by both steady and unsteady 2D incompressible flow problems. Numerical results indicate that the developed implicit method outperforms its explicit counterpart in terms of the convergence property and computational efficiency. The speedup ratio of the computational effort is about 3–22.

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Discrete gas-kinetic scheme-based arbitrary Lagrangian–Eulerian method for moving boundary problems

2021

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In this work, a discrete gas-kinetic scheme (DGKS) based on the arbitrary Lagrangian–Eulerian (ALE) method is proposed for the simulation of moving boundary problems. The governing equations are the ALE-based Navier–Stokes equations, which are discretized using the finite volume method. Starting from a circular function-based Boltzmann equation, a grid motion term is introduced to obtain the Boltzmann equation in ALE form. Based on the moment relations and Chapman–Enskog analysis, the moment of particle velocity and distribution function are summed to obtain the fluxes. The DGKS expression in the ALE framework can then be derived. In this method, the flux at the cell interface can be calculated from the local solution of the Boltzmann equation, which is physically realistic and makes the algorithm more stable. As DGKS is based on a multidimensional particle velocity model, it is not necessary to use approximate values for the reconstruction process. In addition, DGKS can simultaneously handle inviscid and viscous fluxes when simulating viscous flow problems, resulting in a higher degree of consistency. Finally, several moving boundary examples are simulated to validate the ALE-DGKS method. The results show the algorithm was observed to achieve second-order accuracy and can solve moving boundary problems effectively.

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High-order gas kinetic flux solver for simulation of two dimensional incompressible flows

Cited by 9 publications

References 68 publications

Two-stage Fourth-order Gas Kinetic Solver-based Compact Subcell Finite Volume Method for Compressible Flows over Triangular Meshes

Two-stage Fourth-order Gas Kinetic Solver-based Compact Subcell Finite Volume Method for Compressible Flows over Triangular Meshes

A high-order implicit least square-based finite difference-finite volume method for incompressible flows on unstructured grids

Discrete gas-kinetic scheme-based arbitrary Lagrangian–Eulerian method for moving boundary problems

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